The answers given before are quite good. I just want to add a few points based on my own experience that may be relevant.
The author of the question did not specify the field. It is safe to assume however that it is of scientific nature.
Let us begin with pure mathematics. Most of computations in pure mathematics are theoretical computations. Here you want to check thoroughly the computation. As you do the hard work, sometimes you realize the bigger picture sometimes you don't. This means that the theoretical result may be simplified, with painless or easier computations. But in general, you do not know yet. So you have to go through the computations. As a personal example, this happened to me when I read Bigelow's paper on the linearity of the classical braid group. This involved a certain detailed computation. Later on the result was understood on another level that greatly simplified the original computation.
Even in pure maths, it may happen that a computation is an example. The author wants to illustrate some of the theory he's building, or is making a certain point. Even in this case, as a reviewer, I immediately go over the example and try to process the computations, especially if the rest of the paper is very theoretical. Why ? Because examples are the flesh of the theory. Without examples, there is nothing to eat. Examples help understand what motivates the author and conversely every fine author should strive at giving illuminating examples that guide the reader. So if the example involves a computation, I will go over it.
If the computation is related to an aside comment, it is a different issue. But it is relative to the field. If a pure math paper numerically computes some CPU time to convey a rough impression of complexity, this is one thing. If it is a computer science paper, it's an altogether different issue.
A computation may mean very different things for a mathematician, a computer scientist or a physicist.
Ultimately, the decision is up to the reviewer's best judgment. And it should do justice to the paper submitted in the sense that the relevancy/motivation to go over the computation is directly related to the originality of the paper.
This is particularly relevant to cross-field literature or interdisciplinary paper. As a mathematician, I occasionally stumble across common errors or bias in papers in neurosciences. In general I want to be able to reproduce the computation just as my co-author wants to reproduce the experiment.
But equally often, I do have to state that I can review only a few aspects of the paper, since I am not qualified in some other fields. With respect to this particular issue raised by interdisciplinary papers, Ben's last paragraph is sensible.
A final word: errors are common. But somehow, over time, big (and not so big) errors are corrected or neutralized. I mean most errors that have resisted the reviewer's critical reading are either inoffensive or disappear. This is not meant to imply blind reliance of the reviewers or peers. But you should not be excessively guilty either on relying on them, especially if their field of expertise is far from yours.